Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
644 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 644 conjugacy classes of subgroups — too many to draw. Only its 116 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C32×#919 | C2 | semidirect |
| 2. D3×#3745 | C2 | semidirect |
| 3. #11722198 | C2 | semidirect |
| 4. C3×#63655 | C2 | semidirect |
| 5. #11722005 | C2 | semidirect |
| 6. #11722004 | C2 | semidirect |
| 7. #11722001 | C2 | semidirect |
| 12. C33×Q16 | C22 | semidirect |
| 16. C32×D24 | C22 | semidirect |
| 19. C3⋊(C3⋊(C3⋊C16)) | C22 | semidirect |
| 20. C3×C3⋊(C3⋊C16) | C22 | semidirect |
| 23. C3×#919 | D3 | semidirect |
| 28. #63655 | D3 | semidirect |
| 54. C32×Q16 | C2×D3 | semidirect |
| 55. C32×Q16 | C2×D3 | semidirect |
| 66. C3×D24 | C2×D3 | semidirect |
| 72. C3⋊(C3⋊C16) | C2×D3 | semidirect |
| 83. #919 | C3⋊D3 | semidirect |
| 133. C3×Q16 | D32 | semidirect |
| 134. C3×Q16 | C2×C3⋊D3 | semidirect |
| 146. D24 | C2×C3⋊D3 | semidirect |
| 179. C33 | #509 | semidirect |
| 219. Q16 | D3×C3⋊D3 | semidirect |
| 248. C32 | #4914 | semidirect |
| 249. C32 | #5193 | semidirect |
| 282. C3 | #10591038 | semidirect |
| 283. C3 | #10592892 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#919 | 2 |
| D3×#3745 | 2 |
| #11722198 | 2 |
| C3×#63655 | 2 |
| #11722005 | 2 |
| #11722004 | 2 |
| #11722001 | 2 |
| #10592892 | 3 |
| #10591038 | 3 |